The Hoover Dam is approximately rectangular in shape with a height of $230$ m and width of $76$

m$.$ When the water is up to the top of the dam, estimate the pressure at the bottom of the dam and the net

force tending to move it$.$ Assume that water has a constant density of $3$

kg$/$m$1000=$o

$\backslash$rho and there is no water

on the downstream side of the dam. How is the net force affected if the density varies with depth given by

$[])(1$ zho $+=$

$\backslash$alpha

$\backslash$rho

$\backslash$rho $,$ where h is the height of the water, z is the vertical distance from the bottom of the dam,

and $-14$ m$105$

$\backslash$times $=$

$\backslash$alpha